In order to support the ultrashort pulse length characteristic of an ultrafast laser, the laser must possess a total negative group-delay-dispersion, (negative GDD or NGDD) i.e., the sum of the GDD of the laser gain-medium and all cavity components must be negative. In a simple arrangement of a laser cavity and dielectric material therein, such as, a gain medium and a mode locking device, total cavity GDD, for wavelengths less than 1000 nanometers (nm) is usually positive, i.e., shorter wavelength light experiences a higher refractive index and lower group velocity, and lags behind longer wavelength light. This causes lengthening of a laser pulse each round trip and prevents stable, short-pulse operation.
One means of avoiding this is to include one or more NGDD devices having collective negative GDD at least equal to, and preferably greater than, this positive GDD. In many applications, the negative GDD is preferably substantially constant over a wavelength range at least equal to the laser output spectrum, and, if the laser is to be tunable over a range of wavelengths, the NGDD is preferably substantially constant over a range in excess of the tuning range.
Reflective NGDD devices which have been used with prior-art ultrafast lasers include Gires-Tournois Interferometer (GTI) mirrors. A GTI-mirror is a multilayer NGDD-mirror including a reflector, which comprises a stack of alternating high and low refractive index dielectric layers, each layer generally having an optical thickness of one-quarter wavelength (0.25 .lambda. or one QWOT) at about the nominal operating wavelength of the laser, and a single, Fabry-Perot-like "spacer" layer (typically a few half-wavelengths thick) of a dielectric material deposited on the reflector. A partially-reflecting multilayer stack may (optionally) be deposited on the spacer layer. A prior art GTI-mirror typically gives a relatively constant negative GDD over only a relatively narrow wavelength range, for example, about 50.0 nm. In a GTI-mirror, the NGDD is achieved by selective resonant trapping of certain wavelengths in the spacer layer. Such a device is described extensively in a paper "Compression of Femto Second Optical Pulses with Dielectric Multilayer Interferometers", Kuhl et al., IEEE Transactions in Quantum Electronics, QE-22, 1, pp. 182-185, (January 1986).
In U.S. Pat. No. 5,734,503 (Szipocs et al.) multilayer NGDD mirrors described as "chirped mirrors" are disclosed. One disclosed example of such a mirror includes a substrate having a structure of more than 40 layers deposited thereon. In this structure, essentially no two adjacent layers have the same optical thickness. Two materials are used for adjacent layers, one having a relatively high refractive index and the other a relatively low refractive index. Throughout the structure, the optical thickness between adjacent layers is substantial, with optical thickness ratios up to about 2:1 not being uncommon. The thickness of individual layers is computer generated (optimized) from an initial layer system described as "intuitive". Increasing individual layers in thickness from the front to the back of the layer system, i.e., from the outermost layer towards the substrate, or a Fourier transform design is suggested, although no detail of such an initial layer system is disclosed. Optimization is performed simultaneously to a GDD specification and a reflectivity specification.
It is taught that, following optimization, apart from a trend of increasing optical thickness of a "reflective period" from the front to the back of the layer system, the layer system does not have any orderly structure. It is taught that nearly-constant NGDD is achieved without the use of Fabry-Perot or GTI resonant trapping mechanisms in the structure, and results simply from different penetration depths of different wavelengths into the structure. Such a mirror appears to be able to provide constant NGDD over a broader band of wavelengths than a GTI-mirror, for example, up to about 150 nm, at a nominal center wavelength of about 800 nm, for a GDD of -45 fs.sup.2.
Other workers have attempted to provide similar results to the above discussed Szipocs et al. result via a more rational approach to the so-called "chirping" of the mirror structures. Tikhonravov et al. in a paper "To the design and theory of chirped mirrors", Proceedings the OSA Conference on Optical Interference Coatings, Jun. 7-12, 1998, Tucson Ariz., pp 293-5, ISBN 1-55752-549-8, attempts to improve on the design method of Szipocs et al. by considering that the design resolves itself into a mirror portion and a phase-correcting portion. In an example of optimized final structure, however, more than half of the 44 layers of an exemplified design have no identifiable relationship with each other, i.e., are aperiodic, and it is very difficult to determine where a mirror portion ends and a phase-correcting portion begins. In the GDD as a function of wavelength there are peak-to-valley oscillations of up to 10 femtoseconds in a nominal range between about -40 and -50 fs.sup.2. These are described as being inevitable.
In another paper "Design of broadband double-chirped mirrors for generation of sub-10 fs laser pulses", Matuschek et al., Ibid. pp. 296-8, it is disclosed that design is initiated by a structure comprising elements described as a quarter-wave section; a simple-chirp section; a double-chirp section; and an AR-coating section. It is disclosed that, after optimization, the different sections tend to "melt together". A final optimized structure is not shown.
In most ultrafast lasers a compensating NGDD far much greater than the -40 to -60 fs.sup.2 of above described prior art devices is required. This is typically remedied by using multiple such devices or resonator structures which will provide multiple reflections from one or more devices. If this is to be achieved using such devices "intra-cavity", then attention must be paid to limiting reflection losses in the resonator (laser resonant-cavity). In this case, also, oscillations in GDD described in the Tikhonravov et al. paper are of concern, as they are compounded by the multiple reflections.
In most ultrafast lasers, a cavity loss in excess of 1.0% would lead to significant loss of output power. By way of example, in an ultrafast laser having 10% outcoupling, a 1% cavity loss (per round-trip) equates to about 10% loss of output power. Because of this, even if 99.9% reflecting NGDD-mirrors were used, more than about ten intra-cavity reflections therefrom per round-trip would produce significant output-power reduction.
While the above described "chirped" NGDD-mirror appears to achieve desirable NGDD properties over a bandwidth greater than has been achieved in prior-art devices of the GTI type which rely on a wide (thick) resonant-cavity to provide NGDD, it would appear from consideration of optical multilayer theory that the aperiodic structures used to achieve these NGDD properties mirror structure are far from those which would produce the highest possible reflectivity over the broadest bandwidth with the same number of layers of the same materials.
It is well-known to designers of multilayer optical devices that the highest reflectivity that can be obtained, at a particular wavelength, with a group of layers having alternately high and low refractive index is achieved when all layers in the group have the essentially the same optical thickness (an optical thickness ratio of 1:1) of one-quarter wavelength at the particular wavelength. Essentially the same optical thickness, here meaning to the extent that is achievable over a broad wavelength range considering refractive index dispersion in the materials and normal manufacturing tolerances. Departures from the 1:1 ratio will result in a lower reflectivity over a narrower bandwidth.
It would be advantageous to provide multilayer structures which achieved comparable NGDD performance to the Szipocs et al. and other above described "chirped-mirror" structures, while preserving sufficient order in the structures that the magnitude and bandwidth of reflectivity were not unduly compromised by any structural mechanisms or features necessary to provide that NGDD. The present invention provides such structures and methods for designing them.